The eigenvector \(y_{2}\)  corresponds to the second largest eigenvalue \(\beta _{2}\)  of the \(N\times N\)  matrix \(W-\text{diag}(W\cdot u)\) . The largest eigenvalue \(\beta _{1}=1\)  corresponds to the eigenvector \(y_{1}=\frac{1}{\sqrt{N}}u\) . Computing the eigenvector \(y_{2}\)  is equivalent to computing the largest eigenvector of the matrix \(W-\text{diag}(W\cdot u)-\frac{1}{N}\cdot u\cdot u^{T}\) , which can be executed using the power method [1]}, for a given matrix \(W\) , with computational complexity \(O\left(L\right)\) .
